Liquidity Effects of Trading Frequency ( extended version ) . ∗

In this work, we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). The new framework captures very closely the true, micro-level, mechanics of an auction-style exchange. At the same time, it uses the standard abstractions of a continuum-player game to obtain a tractable macro-level description of the LOB. We use the proposed modeling framework to analyze the effects of trading frequency on market liquidity in a very general setting. In particular, we demonstrate the dual effect of high trading frequency. On the one hand, the higher frequency increases market efficiency, if the agents choose to provide liquidity in equilibrium. On the other hand, the higher trading frequency also makes markets more fragile, in the sense that the agents choose to provide liquidity in equilibrium only if they are market-neutral (i.e. their beliefs satisfy certain martingale property). Even a very small deviation from market-neutrality may cause the agents to stop providing liquidity, if the trading frequency is sufficiently high, which represents a self-inflicted liquidity crises (aka flash crash) in the market. This framework allows us to provide more insight into how such a liquidity crisis unfolds, connecting it to the so-called adverse selection effect.